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Atomic electron tomography reveals chemical order in medium- and high-entropy alloys

This is a summary of: Moniri, S. et al . Three-dimensional atomic structure and local chemical order of medium- and high-entropy nanoalloys. Nature 624 , 564–569 (2023) .

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doi: https://doi.org/10.1038/d41586-023-03656-5

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George, E. P., Raabe, D. & Ritchie, R. O. Nature Rev. Mater. 4 , 515–534 (2019).

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Students' representations of the atomic structure – the effect of some individual differences in particular task contexts

George Papageorgiou *, Angelos Markos and Nikolaos Zarkadis Democritus University of Thrace, Greece. E-mail: [email protected]

First published on 9th December 2015

The current study aims to investigate students' representations of the atomic structure in a number of student cohorts with specific characteristics concerning age, grade, class curriculum and some individual differences, such as formal reasoning and field dependence/independence. Two specific task contexts, which were designed in accordance with corresponding teaching contexts for the atomic structure, one based on Bohr's model and the other on the quantum mechanical model, were examined as for their potential to differentiate initial students' representations of the atomic structure (when no specific context was provided). Participants ( n = 421) were students of 8th, 10th and 12th grades of secondary schools from Northern Greece. Results showed that, although developmental factors, like formal reasoning, were associated with a better representation of the atomic structure, the task context appeared to have the dominant role, since positive associations were found between student cohort characteristics and representation of the atomic structure in context dependent tasks, even after accounting for the effects of individual differences.

Introduction

Students' representations of the atomic structure.

However, more interesting are the cases where student models comprise paths of electrons, either with or without references to certain levels of orbits and/or to energy quantization. These cases are reported mostly as the ‘solar system model’ ( Harrison and Treagust, 1996 ; Nicoll, 2001 ; Nakiboglu, 2003 ; Cokelez and Dumon, 2005 ; Cokelez, 2012 ), the ‘planetary model’ ( Petri and Niedderer, 1998 ; Papaphotis and Tsaparlis, 2008 ; Adbo and Taber, 2009 ; Tsaparlis and Papaphotis, 2009 ) or ‘Bohr's model’ ( Fischler and Lichtfield, 1992 ; Nicoll, 2001 ; McKagan et al. , 2008 ; Papaphotis and Tsaparlis, 2008 ; Park and Light, 2009 ; Tsaparlis and Papaphotis, 2009 ; Wang and Barrow, 2013 ), and are considered to be the most typical ones in students' descriptions of the atomic structure. Even though these cases refer to scientifically and historically different models ( Justi and Gilbert, 2000 ), in the majority of students' mental model categorizations as articulated by science education researchers, they have been treated as one and the same kind of deterministic model. For instance, Park and Light (2009) studied students' representations of the atomic structure. Although from a scientific point of view Bohr's model has been clearly based on quantum theory, the researchers incorporated all the above cases – even those without any references to quantum theory – into the same student model, i.e. ‘Bohr's model’. Possible student references to certain levels of orbits and/or energy quantization were taken into account only in the formation of the corresponding sub-categories inside this model. Other researchers, when they similarly blend scientifically different models in order to form a particular student mental model, they use appropriate representative terms, such as ‘planetary Bohr's model’ ( Tsaparlis and Papaphotis, 2009 ) or ‘Bohr/solar system model’ ( Stevens et al. , 2010 ). In any case, this kind of mental model – let us refer to it as ‘Bohr's model’ – appears to be the most dominant in students' thinking, even in the upper grades of secondary education, where the conditions could probably facilitate the development of a more sophisticated approach to the atomic structure ( Fischler and Lichtfield, 1992 ; Petri and Niedderer, 1998 ; Papaphotis and Tsaparlis, 2008 ; Tsaparlis and Papaphotis, 2009 ).

Towards a quantum description of the atomic structure, the literature shows more sophisticated students' representations that are reported as ‘orbital model’ ( Harrison and Treagust, 1996 ; Kalkanis et al. , 2003 ; Taber 2005 ), ‘electron cloud model’ ( Petri and Niedderer, 1998 ; Cokelez and Dumon, 2005 ; Tsaparlis and Papaphotis, 2009 ; Stevens et al. , 2010 ; Cokelez, 2012 ), ‘quantum model’ ( Taber, 2002a, 2005 ; Park and Light, 2009 ) or ‘Schrödinger model’ ( McKagan et al. , 2008 ). In these student models, concepts such as energy quantization, wave function or/and probability are frequently present. Similar to those reported above for ‘Bohr's model’, an incorporation of scientifically different relevant models into a particular student mental model has also been noticed – let us refer to it as the ‘quantum mechanical model’. However, research has demonstrated that students generally have difficulties and hold misconceptions in adopting this model, since its understanding also requires an understanding of many other abstract concepts such as ‘orbital’ ( Tsaparlis, 1997 ; Taber, 2002a, 2002b, 2005 ; Tsaparlis and Papaphotis, 2002, 2009 ; Nakiboglu, 2003 ; Papaphotis and Tsaparlis, 2008 ; Stefani and Tsaparlis, 2009 ), ‘electron cloud’ ( Harrison and Treagust, 1996, 2000 ; Tsaparlis and Papaphotis, 2002, 2009 ), ‘quantization of energy’ and ‘angular momentum’ ( Taber, 2002a ; Didiş et al. , 2014 ), ‘probability’ ( Park and Light, 2009 ), ‘Heisenberg's uncertainty principle’ ( Tsaparlis and Papaphotis, 2009 ) and other characteristics of a quantum probabilistic approach.

The effect of the context

However, apart from the implications for the teaching/learning procedure, the idea that these two models ( i.e. ‘Bohr's model’ and the ‘quantum mechanical model’) define two different contexts has also implications for researchers trying to explore relevant students' representations. In the process of developing an appropriate research instrument and creating certain tasks, a researcher has the option to define a ‘task context’ with particular contextual features/settings, on which students could base their representations of the atomic structure. In other words, ‘task context’ refers to a set of situational settings in a specific area, in which cueing and prompting are given to students ( Sağlam, 2010 ). The question here is: Could such a task context have a significant effect on the corresponding student's representation?

According to a number of studies, a ‘task context’ can generally affect student responses ( e.g. Palmer, 1997 ; Petri and Niedderer, 1998 ; Bao et al. , 2002 ; Itza-Ortiz et al. , 2004 ; Bao and Redish, 2006 ; Redish and Smith, 2008 ; Teichert et al. , 2008 ; Hrepic et al. , 2010 ; Sağlam, 2010 ; Didiş et al. , 2014 ). This is known as ‘context dependence’ ( e.g. Bao and Redish, 2006 ; Redish and Smith, 2008 ) and it is also connected to the theory of ‘knowledge in pieces’ ( diSessa, 1993 ). According to the latter, student responses to particular questions are based on the ‘ in situ ’ combination of small pieces of knowledge that could produce inconsistent answers, since they are influenced by the contextual features of the questions. On this basis, when students are trying to work within two different task contexts towards a representation of the atomic structure, they could activate different knowledge resources, which would significantly differentiate their thinking. For example, in the study of Tsaparlis and Papaphotis (2009) on students' atomic representations, it appears that the context of the tasks during the interviews and the relevant discussions affected the high-school students' (12th grade) representations, leading those who initially provided simple model representations ( e.g. Bohr model) to adopt a more sophisticated model (electron cloud model). Such context dependence could be affected by a number of factors. Wang and Barrow (2013) , for instance, when investigated the undergraduate students' general chemistry conceptual frameworks about the atomic structure, found that ‘high conceptual knowledge’ (HCK) students were much more context dependent than ‘low conceptual knowledge’ (LCK) students. HCK students had the ability to adapt their representations of the atomic structure to the context of the task and thus, could switch from the Bohr model to the electron-cloud model using quantum mechanics descriptions in order to explain, for instance, the electron distribution of a polar bond. In contrast, LCK students could only work on simple models and had difficulties in using quantum mechanics descriptions in the context of the electron-cloud model.

Individual differences

Formal Reasoning (FR), also reported as Logical Thinking , is in fact a Piagetian concept and it refers to the ability of an individual to use concrete and formal operational reasoning ( Lawson, 1978, 1985, 1993 ). In the general context of science education many studies have reported a correlation between FR and student performance ( e.g. Lawson, 1982 ; Chandran et al. , 1987 ; Niaz, 1996 ). On the other hand, Field Dependence/Independence (FDI) is associated with the ability of an individual to disembed relevant information from a complex context or, in other words, the ability to efficiently separate the ‘signal’ from the ‘noise’ ( Witkin et al. , 1971 ). In the literature, FDI appears to be very important for the conceptual understanding of science concepts ( Bahar and Hansell, 2000 ; Kang et al. , 2005 ; Tsaparlis, 2005 ; Danili and Reid, 2006 ).

The atomic structure in Greek secondary education

Particularly relevant to the context of chemistry, students in the 8th grade receive a one-hour lesson per week about (among others) the concept of the atom, the subatomic particles and their characteristics, as well as an introduction to Bohr's atomic model. In the 10th grade, during two one-hour lessons per week, students are taught the electronic configuration of the atom based on Bohr's atomic model. In the 12th grade, students in the ‘science and math’ direction also receive two one-hour lessons per week, where they are taught (among others) the quantum mechanical model and relevant concepts, such as the atomic orbital, the uncertainty principle, the electron cloud and its density.

In the context of physics, all students of the 12th grade receive a one-hour lesson per week, where they are taught (among others) more in-depth concepts related to the Bohr atomic model, such as the electron stimulation or the ionization.

Rationale of the study and research questions

With regard to individual differences, choices were theory driven considering also previous research findings. According to those, a number of Neo-Piagetian cognitive variables are identified as predictors of student achievement in science ( Johnstone and Al-Naeme, 1995 ; Niaz, 1996 ; Tsitsipis et al. , 2010 ). Among them, formal reasoning and field dependence/independence were sought as closely associated with the tasks usually involved in the learning process related to science topics ( Tsitsipis et al. , 2010 ; Stamovlasis and Papageorgiou, 2012 ), especially those for which ‘context’ is an issue.

Thus, the present study aims to investigate:

1. What are the students' representations of the atomic structure, in both the presence and absence of task context?

2. To what extent do cognitive factors ( i.e. individual differences concerning formal reasoning and field dependence/independence) and student cohort characteristics (grade, age and curriculum) explain a possible variability in student competence for representing the atomic structure in the presence and absence of a task context?

Taking into account recent relevant research evidence, a number of hypotheses could be articulated:

• Hypothesis 1 : It is expected that a task context will have a significant impact on students' representations of the atomic structure and consequently, representations will differ when the context changes.

• Hypothesis 2 : It is expected that dependent on or independent of a task context, an increase in the odds of possessing a scientifically sufficient representation will be associated with an increase in formal reasoning, field dependence/independence and student cohort characteristics (age and grade).

• Hypothesis 3 : In line with the literature ( e.g. Wang and Barrow, 2013 ), it is expected that student cohort characteristics will be associated with representations, even after accounting for the effects of cognitive factors.

Methodology

Subjects and procedure, instruments.

The construct validity of the two cognitive constructs was examined in the context of Confirmatory Factor Analysis (CFA). Due to the dichotomous/categorical nature of the test items (the correct and incorrect dichotomy was obtained by collapsing the options representing the wrong alternatives) the analysis was performed on the tetrachoric correlation matrix using the WLSMV (Weighted Least Squares with Mean and Variance Adjustment) estimator implemented in Mplus software Version 7.31 ( Muthén and Muthén, 2012 ). The model fit was evaluated using the following indices: comparative fit index (CFI), Tucker–Lewis index (TLI), root mean square error of approximation (RMSEA), and 90% confidence interval (CI) of RMSEA. According to previous research, CFI and TLI values ≥0.95 and RMSEA values ≤0.08 were considered as good indicators of the data-model fit ( Hu and Bentler, 1999 ). Internal consistency of all measures was assessed using Cronbach's alpha coefficient. Scores for all scales used in the study were computed by summing the items that constitute the scale.

Table 1 summarizes the descriptive statistics of each one of the cognitive scales.

Students' representations were assessed in all tasks, taking into account both drawings and relevant feature descriptions, according to their correctness and completeness in comparison to the scientific view. Student scoring categorization took into account other similar categorizations already presented in relevant research ( e.g. , Harrison and Treagust, 1996 ; Park and Light, 2009 ; Cokelez, 2012 ). A summary of the categories for all tasks is presented in Table 3 together with the corresponding sub-categories. Category E refers to the most scientifically sufficient, whereas A refers to the most naïve.

In fact, the two contexts of tasks 2a and 2b could potentially lead students towards categories D and E, respectively. So, a shift from categories A, B and C to category D was expected in task 2a and a shift from categories A, B, C and D to category E in task 2b. Of course, this does not mean that all students shifting to D or E could fully understand the corresponding model, i.e. Bohr's model in task 2a and the quantum mechanical model in task 2b; what was assessed in that case was the ability of students to adapt their representations of the atomic structure within the given characteristics of a specific context. A possible shift from E to D in task 2a could also not be excluded.

Statistical analysis

In order to investigate the influence of student cohort characteristics on students' representations, after accounting for the effects of cognitive variables (hypothesis 3), a Categorical Regression Analysis model (CATREG in SPSS) was examined with student cohort characteristics as the outcome and the two cognitive factors as the independent variables. The model residuals were subsequently correlated with students' representations using Kendall's tau-b correlation coefficient.

Preliminary analyses

With regard to the context dependent tasks (2a and 2b), shifts towards categories D and E were observed ( Table 4 ). In task 2a, as expected, the majority of students appeared to be affected by the characteristics of the corresponding context and they represented the atomic structure according to Bohr's model (65.8%), although the nuclear model still held a significant percentage (26.6%). A closer look at the distribution per student cohort ( Table 5 ) revealed that the effect of a task context was greater in the 3rd and 4th cohorts, where 92.7% and 91.1% of students of each one of these cohorts, respectively, responded within the Bohr's model.

Interestingly, the effect of context on students' representations was even more obvious in task 2b, where the quantum mechanical model reached unexpectedly a percentage of 43.5% of the sample. The effect was even larger in the 4th cohort, reaching 93.3% of the students of this particular cohort. Taking into account the difficulty in perceiving the characteristics of this model, which also justifies the high percentage of missing values, these figures seem to be higher than expected. However, one should also take into account that this cohort included students who had been taught this model. In addition, as already mentioned, this does not mean that all these students have developed a good knowledge of the quantum mechanical model.

Results of ordinal logistic regression

Student cohort characteristics had also a statistically significant effect ( χ 2 (3) = 15.820, p = 0.001). Specifically, the odds for the 4th cohort (12th grade students – science and math direction) of possessing a sufficient representation of the atomic structure in task 1 were (1/0.270) = 3.70 times greater than the odds for the 1st cohort (8th grade students), (1/0.214) = 4.67 times higher than the odds for the 2nd cohort (10th grade students) and (1/0.289) = 3.46 times higher than the odds for the 3rd cohort (12th grade students – technological direction). In contrast, the odds of the 2nd cohort and the 3rd cohort were similar to those of the 1st cohort. Finally, the odds for the 3rd cohort were similar to those of the 2nd cohort. All the effects were found to be statistically significant.

However, student cohort characteristics had a statistically significant effect ( χ 2 (3) = 27.230, p < 0.001). The odds for the 4th cohort of possessing a sufficient representation of the atomic structure in task 2a were (1/0.034) = 29.41 times greater than the odds for the 1st cohort, (1/0.062) = 16.12 times higher than the odds for the 2nd cohort and (1/0.220) = 4.54 times higher than the odds for the 3rd cohort. The odds for the 2nd cohort were 1.82 times greater than the odds for the 1st cohort. Finally, the odds for the 3rd cohort were 4.54 and 3.56 times greater than the odds for the 1st and 2nd cohorts. All the effects were statistically significant.

Student cohort characteristics had also a statistically significant effect ( χ 2 (3) = 12.899, p = 0.005). The odds for the 4th cohort of possessing a sufficient representation of the atomic structure in task 2b were (1/0.322) = 3.10 times greater than the odds for the 1st cohort, (1/0.184) = 5.43 times higher than the odds for the 2nd cohort and (1/0.223) = 4.48 times higher than the odds for the 3rd cohort. Moreover, the odds of the 2nd cohort were 1.95 times greater than that for the 1st cohort. Lastly, the odds for the 3rd cohort are 5.44 and 7.12 times greater than the odds for the 1st and the 2nd cohorts, respectively. All the effects were statistically significant.

Finally, the unique influence of student cohort characteristics on the representations of the atomic structure, after accounting for the effects of formal reasoning and field dependence/independence was investigated. For this purpose, the residuals of a categorical regression analysis model with cohort characteristics as the dependent variable and the two cognitive factors (FR and FDI) as independent were correlated with student performance in each of the three tasks, using Kendall's tau-b correlation coefficient. A non-significant correlation was detected for context independent task 1 (tau-b = 0.061, p > 0.05), whereas for context dependent tasks 2a and 2b the correlations were found to be positive and statistically significant (tau-b = 0.177 and tau-b = 0.192, p < 0.01). These results indicate, in the case of context dependent tasks, a positive association between student cohort characteristics and possessing a sufficient representation of the atomic structure, even after controlling for the effects of formal reasoning and field dependence/independence.

Discussion and educational implications

The effect of a task context.

With regard to hypothesis 1, it was expected that students' representations would change when students had to work within specific characteristics of particular task contexts. Indeed, the effect of such contexts was found to be significant for both tasks 2a and 2b. In the Bohr's context (task 2a) students reached very high percentages, which were higher than 90% in 3rd and 4th cohorts. Rather unexpectedly, it was observed that in task 2b (quantum mechanical context), students of the 4th cohort were not the only ones affected by the context (very high percentage, 93.3%), but significant percentages of students in the other cohorts were affected as well. Although possible implications for the corresponding teaching context is a big step ahead, one could make speculations for the possibility to have analogous effects on the adoption of more sophisticated models by students through an appropriately designed teaching/learning process. Relevant research provides evidence to this direction. Petri and Niedderrer (1998), for instance, when differentiated the teaching context by setting different teaching inputs during a series of 80 appropriately designed lessons for the atomic structure, they found that, despite the domination of the planetary model in students' representations, different inputs had as a result the development of different conceptions for the atom, moving to a significant degree, from the planetary model to the electron cloud model.

The effect of individual differences

Consequently, the findings concerning individual differences address to anyone who can configure the ‘teaching context’ and especially, to teachers and science curriculum designers. As has been suggested elsewhere ( e.g. , Stamovlasis and Papageorgiou, 2012 ), both of them can improve teaching outcomes, by adapting teaching context and relevant subject matter to the understanding level of the students of each grade and by using appropriately designed means, such as illustrations, diagrams, and representations, in order to stimulate student attention on critical attributes of the atomic structure, especially when this is studied through more sophisticated models.

The effect of student cohorts

Conclusions.

As for the implications for the teaching and learning process, although the effect of a ‘task context’ does not necessarily imply direct analogous effects of ‘teaching context’, some general considerations could be possibly made. In that context, it appears that, although developmental factors, like formal reasoning, will always play an important role in the learning process, having a significant effect on students' representations and conceptions in general, the success of this process is actually defined by the role of the teacher and the curricula designers. A science curriculum that takes into account student characteristics in each grade and an appropriate teaching methodology on the basis of a compatible context could potentially overcome the challenges that arise by other factors, like FDI, and drive students through learning paths.

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Editorial article, editorial: the future of nuclear structure: challenges and opportunities in the microscopic description of nuclei.

• 1 Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Napoli, Italy
• 2 Physics Department and McDonnell Center for the Space Sciences at Washington University in St. Louis, St. Louis, MO, United States
• 3 Department of Physics, University of Surrey, Guildford, United Kingdom
• 4 Dipartimento di Fisica, Universita Degli Studi di Milano, Milano, Italy
• 5 INFN, Sezione di Milano, Milano, Italy

Editorial on the Research Article The Future of Nuclear Structure: Challenges and Opportunities in the Microscopic Description of Nuclei

The past two decades have witnessed tremendous progress in the microscopic description of atomic nuclei. Within this approach, nuclei are described in terms of nucleons interacting via realistic two- and three-body forces, constrained to accurately reproduce a large body of data for few nucleons systems. The goal of the nuclear theory community is to gain an accurate and predictable understanding of how the properties of many-body systems, along with their dynamics and structure, emerge from internucleon correlations induced by the strong interaction.

Progress in the microscopic (or, ab initio ) theory has been quite notable and it has been supported by two major pillars: First, thanks to the advent of Effective Field Theories (EFTs), we can now systematically develop nuclear Hamiltonians that are rooted in the fundamental properties and symmetries of the underlying theory of QCD. Second, advances in computational resources and novel powerful algorithms allow us to solve 1) the many-nucleon problem efficiently, and 2) quantify the degree of reliability of theoretical calculations and predictions. In many cases, microscopic computations achieve an accuracy that is comparable or superior to the precision delivered by current EFT interactions. This sparked a renewed interest to further broaden the focus of ab initio theory and address open problems in nuclear physics.

While the status of the first pillar has been recently discussed by “The Long-Lasting Quest for Nuclear Interactions: The Past, the Present and the Future” Topical Review on this Journal, here we focus on the exciting new developments in microscopic theory. At present, ab initio computations of nuclear structure include up to medium-mass isotopes. The heaviest systems currently reached—with different degrees of accuracy—have mass number A ≈ 140 . These computational limits are constantly being pushed forward. At the same time, the community is expanding into new directions, in particular toward the study of electroweak observables and nuclear reactions, that nowadays require predictions with an accuracy never reached before for similar mass ranges.

In collecting the contributions for this Research Topic, we sought to gather contributions from authors who could summarize the current state-of-the-art microscopic calculations in Nuclear Theory, favoring a selected but broad view over an attempt to cover every application. All presented contributions stem from well-established methods in computational nuclear structure, and indicate recent theoretical advances and prospective outlooks, challenges and opportunities for Nuclear Theory. Most importantly, it is our hope that this collection will confer a big picture, including references to basic material, that will be valuable for young researches who intend to enter this exciting discipline.

The richness of applications in modern ab initio nuclear theory can be appreciated in Hergert ’s contribution that provides us with a general overview of the most successful microscopic many-body approaches currently in use. Traditionally, the refinement and sophistication of these computational tools has given fundamental support to advance the theories of nuclear forces. Quantum Monte Carlo (QMC) techniques allow to solve the many-body Schrödinger equation with high accuracy for light nuclei up to masses A ∼ 16–40. Gandolfi et al. discuss the use of QMC methods (namely, Variational, Green’s Function, and Auxiliary Diffusion Monte Carlo methods) in combination with local chiral interactions in coordinate space. QMC methods are used in lattice effective field theory, where the EFT Lagrangian is implemented in momentum space with nucleons and pions placed on a lattice. Lee discusses the basic features of this approach and its high potential for understanding clustering phenomena.

For heavier isotopes, ab initio theories can be pushed to masses A ∼ 140 provided that one retains only the relevant nuclear excitations, as it is done through all-orders resummations. Among these methods, the self-consistent Green’s function (SCGF) theory gives direct access to the spectral information probed by a wide range of experiments as reviewed in detail by Somà ’s contributions. Once in the region of the nuclear chart that corresponds to medium masses, open shell isotopes become the next challenge to be addressed by the theory. In fact, resolving the degeneracy in uncorrelated systems requires large scale configuration mixing. Coraggio and Itaco demonstrate how this can be handled by projecting the correlated many-body states into a shell model Hamiltonian, using the so-called “Q-box” formalism. A similar strategy is shared by other computational frameworks, such as coupled cluster and in-medium SRG, that are touched upon in the contribution by Hergert . A less conventional approach to open shells is to break SU(1) symmetry (in short, allowing for breaking particle number conservation). This is discussed by Somà within SCGFs and by Tichai et al. in the framework of many-body perturbation theory.

The remainder of this topical review focuses on selected open challenges in Nuclear Theory that require an ab initio approach. Two contributions show different aspect of studying infinite nucleon systems and the implications for astrophysical scenarios. Tews covers QMC calculations of the equation of state (EoS) of dense matter in neutron stars. With the recent observation of star mergers and the birth of multi-messenger astronomy, it has become of prime importance to understand the finite temperature properties of the EoS. Rios discusses this topic and how the structure of neutron matter depends on temperature, using SCGF theory.

In the quest for physics beyond the Standard Model, Nuclear Theory, and in particular accurate calculations of neutrino-nucleus interactions at all energy scaler, plays a crucial role. This is carefully analyzed by Rocco ’s contribution that address this challenge with emphasis on impacts to neutrino oscillations experimental programs. The last contribution of this Topical Review addresses one of the hardest open challenges in the interpretation of experimental data: the lack of a truly first-principles theory that can describe consistently both structure and reaction processes. Rotureau highlights recent steps in deriving an ab inito optical potential using the coupled cluster method (that, together with SCGF, is one of the two possible approaches to this problem).

We are really grateful to all the scientists participating in this project and hope that the reader will enjoy this Topical Review.

Author Contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The handling editor declared a past co-authorship with one of the authors SP.

Keywords: Ab initio (calculations), nuclear theory, nuclear reactions, effective field theories, many-body physics, nuclear structure

Citation: Coraggio L, Pastore S and Barbieri C (2021) Editorial: The Future of Nuclear Structure: Challenges and Opportunities in the Microscopic Description of Nuclei. Front. Phys. 8 :626976. doi: 10.3389/fphy.2020.626976

Received: 07 November 2020; Accepted: 20 November 2020; Published: 05 February 2021.

Edited and Reviewed by:

Copyright © 2021 Coraggio, Pastore and Barbieri. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Luigi Coraggio, [email protected] ; Saori Pastore, [email protected] ; Carlo Barbieri, [email protected]

This article is part of the Research Topic

The Future of Nuclear Structure: Challenges and Opportunities in the Microscopic Description of Nuclei

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2.2: Atomic Structure

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Learning Objectives

• State the modern atomic theory.
• Learn how atoms are constructed.

The smallest piece of an element that maintains the identity of that element is called an atom . Individual atoms are extremely small. It would take about fifty million atoms in a row to make a line that is 1 cm long. The period at the end of a printed sentence has several million atoms in it. Atoms are so small that it is difficult to believe that all matter is made from atoms—but it is.

The concept that atoms play a fundamental role in chemistry is formalized by the modern atomic theory , first stated by John Dalton, an English scientist, in 1808. It consists of three parts:

• All matter is composed of atoms.
• Atoms of the same element are the same; atoms of different elements are different.
• Atoms combine in whole-number ratios to form compounds.

These concepts form the basis of chemistry. Although the word atom comes from a Greek word that means "indivisible," we understand now that atoms themselves are composed of smaller parts called subatomic particles . The first part to be discovered was the electron , a tiny subatomic particle with a negative charge. It is often represented as e − , with the right superscript showing the negative charge. Later, two larger particles were discovered. The proton is a more massive (but still tiny) subatomic particle with a positive charge, represented as p + . The neutron is a subatomic particle with about the same mass as a proton, but no charge. It is represented as either n or n 0 . We now know that all atoms of all elements are composed of electrons, protons, and (with one exception) neutrons. Table \(\PageIndex{1}\) summarizes the properties of these three subatomic particles.

How are these particles arranged in atoms? They are not arranged at random. Experiments by Ernest Rutherford in England in the 1910s pointed to a nuclear model with at oms that has the protons and neutrons in a central nucleus with the electrons in orbit about the nucleus . The relatively massive protons and neutrons are collected in the center of an atom, in a region called the nucleus of the atom (plural nuclei ). The electrons are outside the nucleus and spend their time orbiting in space about the nucleus. (Figure \(\PageIndex{1}\)).

The modern atomic theory states that atoms of one element are the same, while atoms of different elements are different. What makes atoms of different elements different? The fundamental characteristic that all atoms of the same element share is the number of protons . All atoms of hydrogen have one and only one proton in the nucleus; all atoms of iron have 26 protons in the nucleus. This number of protons is so important to the identity of an atom that it is called the atomic number. The number of protons in an atom is the atomic number of the element. Thus, hydrogen has an atomic number of 1, while iron has an atomic number of 26. Each element has its own characteristic atomic number.

Atoms of the same element can have different numbers of neutrons, however. Atoms of the same element (i.e., atoms with the same number of protons) with different numbers of neutrons are called isotopes . Most naturally occurring elements exist as isotopes. For example, most hydrogen atoms have a single proton in their nucleus. However, a small number (about one in a million) of hydrogen atoms have a proton and a neutron in their nuclei. This particular isotope of hydrogen is called deuterium. A very rare form of hydrogen has one proton and two neutrons in the nucleus; this isotope of hydrogen is called tritium. The sum of the number of protons and neutrons in the nucleus is called the mass number of the isotope.

Neutral atoms have the same number of electrons as they have protons, so their overall charge is zero. However, as we shall see later, this will not always be the case.

Example \(\PageIndex{1}\):

• The most common carbon atoms have six protons and six neutrons in their nuclei. What are the atomic number and the mass number of these carbon atoms?
• An isotope of uranium has an atomic number of 92 and a mass number of 235. What are the number of protons and neutrons in the nucleus of this atom?
• If a carbon atom has six protons in its nucleus, its atomic number is 6. If it also has six neutrons in the nucleus, then the mass number is 6 + 6, or 12.
• If the atomic number of uranium is 92, then that is the number of protons in the nucleus. Because the mass number is 235, then the number of neutrons in the nucleus is 235 − 92, or 143.

Exercise \(\PageIndex{1}\)

The number of protons in the nucleus of a tin atom is 50, while the number of neutrons in the nucleus is 68. What are the atomic number and the mass number of this isotope?

Atomic number = 50, mass number = 118

When referring to an atom, we simply use the element's name: the term sodium refers to the element as well as an atom of sodium. But it can be unwieldy to use the name of elements all the time. Instead, chemistry defines a symbol for each element. The atomic symbol is a one- or two-letter representation of the name of an element. By convention, the first letter of an element's symbol is always capitalized, while the second letter (if present) is lowercase. Thus, the symbol for hydrogen is H, the symbol for sodium is Na, and the symbol for nickel is Ni. Most symbols come from the English name of the element, although some symbols come from an element's Latin name. (The symbol for sodium, Na, comes from its Latin name, natrium .) Table \(\PageIndex{2}\) lists some common elements and their symbols. You should memorize the symbols in Table \(\PageIndex{2}\), as this is how we will be representing elements throughout chemistry.

The elements are grouped together in a special chart called the periodic table of all the elements . A simple periodic table is shown in Figure \(\PageIndex{2}\), while one may view a more extensive periodic table from another source. The elements on the periodic table are listed in order of ascending atomic number. The periodic table has a special shape that will become important to us when we consider the organization of electrons in atoms (Chapter 8). One immediate use of the periodic table helps us identify metals and nonmetals. Nonmetals are in the upper right-hand corner of the periodic table, on one side of the heavy line splitting the right-side part of the chart. All other elements are metals.

There is an easy way to represent isotopes using the atomic symbols. We use the construction:

\[\ce{_{Z}^{A}X}\nonumber \]

where \(X\) is the symbol of the element, \(A\) is the mass number, and \(Z\) is the atomic number. Thus, for the isotope of carbon that has 6 protons and 6 neutrons, the symbol is:

\[\ce{_{6}^{12}C}\nonumber \]

where \(C\) is the symbol for the element, 6 represents the atomic number, and 12 represents the mass number.

Example \(\PageIndex{2}\):

• What is the symbol for an isotope of uranium that has an atomic number of 92 and a mass number of 235?
• How many protons and neutrons are in \(\ce{_{26}^{56}Fe}\)
• The symbol for this isotope is \(\ce{_{92}^{235}U}\)
• This iron atom has 26 protons and 56 − 26 = 30 neutrons.

Exercise \(\PageIndex{2}\)

How many protons are in \(\ce{_{11}^{23} Na}\)

It is also common to state the mass number after the name of an element to indicate a particular isotope. Carbon-12 represents an isotope of carbon with 6 protons and 6 neutrons, while uranium-238 is an isotope of uranium that has 146 neutrons.

A Short History of the Atomic Structure

The basic idea that matter is made up of tiny indivisible particles is very old, appearing in many ancient cultures such as Greece and India. The word  atom  is derived from the ancient Greek word  atomos , which means "indivisible".  This ancient idea was based on philosophical reasoning rather than scientific reasoning, and modern atomic theory was developed throughout a few centuries of research and experimentation.

The first atomic theory based on experimentation was stated by John Dalton, an English scientist, in 1808. By studying the chemical composition of different oxides, Dalton noticed that elements combined in very specific patterns given by small whole numbers. This observation prompted him to support that all matter is made of atoms, although Dalton had no idea about the actual structure of the atoms.

In 1897, J. J. Thomson discovered that the existence of the first  subatomic  particle. He renamed these new negatively charged particles as  electrons . To explain the overall neutral charge of the atom, Thomson concluded that these electrons must be embedded in an uniform sea of positive charge. In this "plum pudding atomic model", the electrons were seen as embedded in the positive charge like raisins in a plum pudding.

Between 1908 and 1913, Ernest Rutherford and his colleagues Hans Geiger and Ernest Marsden came to have doubts about the Thomson model.  Rutheford performed a series of experiments in which they bombarded thin foils of metal with positively charged alpha particles. They spotted alpha particles being deflected by angles greater than 90°. To explain this, Rutherford proposed that the positive charge of the atom is not distributed throughout the atom's volume as Thomson believed, but is concentrated in a tiny nucleus at the center. Rutherford's atomic model introduced the existence of the positively charged nucleus surrounded by the negatively charged electrons.

In 1913, after studying atomic spectra produced by elements. the physicist Niels Bohr proposed a model in which the electrons of an atom were assumed to orbit the nucleus but could only do so in a finite set of orbits, and could jump between these orbits only in discrete changes of energy corresponding to absorption or radiation of a photon. This quantized atomic model, also known as the planetary model of the atom, was used to explain why the electrons' orbits are stable and why elements absorb and emit electromagnetic radiation in discrete lines. The Bohr model of the atom was the first complete physical model of the atom. It described the overall structure of the atom and how atoms bond to each other. Bohr's planetary atomi model was not perfect and was soon superseded by the more accurate Schrödinger model, but it is sufficient to understand most chemical and physical properties discussed in this course.

In 1924, Louis de Broglie had proposed that all particles behave like waves to some extent, including the electron. In 1926 Erwin Schrödinger used this idea to develop the Schrödinger model of the atom. In this model, electrons are considered electromagnetic waves mechanics rather than particles. According to this model, it is mathematically impossible to obtain precise values for both the position and the energy (momentum) of an electron at a given point in time. This idea became the uncertainty principle, formulated by Werner Heisenberg in 1927. Because it is impossible to determine the position and the energy of an electron in an atom, Schrödinger's atomic model is based on the "probability" of finding an electron in a certain region around the nucleus. Thus, the orbits in the planetary model of the atom were discarded in favor of atomic orbitals, which are zones around the nucleus where a given electron is most likely to be observed.

Figure \(\PageIndex{2}\):A summary of atomic models. Image by Compound Interest (2016)  https://www.compoundchem.com/2016/10/13/atomicmodels/. Shared under  CC BY-NC-ND 4.0   license

Key Takeaways

• Chemistry is based on the modern atomic theory, which states that all matter is composed of atoms.
• Atoms themselves are composed of protons, neutrons, and electrons.
• Each element has its own atomic number, which is equal to the number of protons in its nucleus.
• Isotopes of an element contain different numbers of neutrons.
• Elements are represented by an atomic symbol.
• The periodic table is a chart that organizes all the elements.

Citations and attributions

" Atomic Theory" by LibreTexts is licensed under CC BY-NC-SA .

Wikipedia contributors. (2021, May 6). Atom. In  Wikipedia, The Free Encyclopedia . Retrieved 15:20, May 18, 2021, from  https://en.wikipedia.org/w/index.php?title=Atom&oldid=1021695004

Wikipedia contributors. (2021, May 8). J. J. Thomson. In  Wikipedia, The Free Encyclopedia . Retrieved 15:21, May 18, 2021, from  https://en.wikipedia.org/w/index.php?title=J._J._Thomson&oldid=1022092604

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Historical Teaching of Atomic and Molecular Structure

• First Online: 30 December 2013

Cite this chapter

• José Antonio Chamizo 2 &
• Andoni Garritz 2  

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Besides the presentation and conclusions, the chapter is divided into two equally important sections. The first one describes the modern development of atomic and molecular structure, emphasising some of the philosophical problems that have been taken, and those that have to be faced in its understanding. The second discusses the alternative conceptions and difficulties of students of different educational levels and also the different approaches to its historical or philosophical teaching. Finally, we recognise the necessity for science teachers to assume a specific historical-philosophical position.

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Chamizo, J.A., Garritz, A. (2014). Historical Teaching of Atomic and Molecular Structure. In: Matthews, M. (eds) International Handbook of Research in History, Philosophy and Science Teaching. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7654-8_12

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Niels Bohr’s First 1913 Paper: Still Relevant, Still Exciting, Still Puzzling

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Kenneth W. Ford; Niels Bohr’s First 1913 Paper: Still Relevant, Still Exciting, Still Puzzling. Phys. Teach. 1 November 2018; 56 (8): 500–502. https://doi.org/10.1119/1.5064553

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Many teachers like to introduce the Bohr atom toward the end of an introductory physics course. This is an excellent idea, given the historic importance of Bohr’s 1913 work, which provided the bridge from Planck’s quantized interaction of matter and radiation (1900) to the full theory of quantum mechanics (1925-28). Unfortunately, the version of the Bohr atom that appears in many textbooks and is no doubt often presented to students is more wrong than right and may leave both teachers and students wondering why, more than a hundred years later, it is still being taught. This “pedagogic” version postulates that an electron in a stationary state moves in a circular orbit with an angular momentum that is an integral multiple of h /2π ( L = nh /2π = nħ )— ħ for the lowest-energy state, 2 ħ for the next state, and so on. This picture of the hydrogen atom is wrong in two senses. First it doesn’t conform to our present understanding of the hydrogen atom. This, in itself, is not a reason to scrap it, for the historical development of quantum physics is certainly of interest. But second, it doesn’t conform to the essence of what Bohr actually did. That is a reason not to teach about circular orbits and L = nħ .

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Atomic physics seeks to understand and control the quantum behavior of matter at the smallest scale. What are the fundamental properties of single atoms, ions, molecules, and photons? Once we combine them together, what are the laws governing emergent many-body phenomena such as superfluidity and magnetism? Can we create and study new states of matter that have never existed in nature before? And how can we exert control over quantum properties to engineer useful systems such as precise clocks, new sensors, fundamentally improved measurements, and new paradigms of quantum computation?

At MIT, researchers trap and manipulate individual ions, photons, spins, and clouds of atoms and molecules. They cool gases down to temperatures a million times colder than deep space, control and image matter at the level of single atoms, hunt for dark matter, tame single photons of light, and control atom-light interactions to generate entanglement and correlations among quantum particles. This research is made possible by an ever-expanding atomic physics toolbox, including ultra-stable lasers, atom and ion traps, nanofabrication of photonic structures, high-resolution microscopes, and optical tweezers.

The group is anchored by the NSF Center for Ultracold Atoms (CUA), a joint effort between atomic physicists at MIT and Harvard, and is also vitally involved in educational activities.

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